The field of the disclosure relates to systems and methods for medical imaging. More particularly, the disclosure relates to systems and methods for creating quantitative images from images that inherently lack or lack complete quantitative information, such a magnetic resonance imaging (“MRI”) images.
Quantitative MRI applications typically involve the acquisition of a series of images, from which physiological parameters are estimated by fitting information in the images to physics-based models. Common examples of quantitative MRI applications include diffusion imaging, perfusion imaging, relaxometry, and elastography. Unlike imaging modalities such as digital photography, images are not directly observed in MRI. Rather, samples of spatial-spectral transformations of the images-of-interest are collected. MRI data is also routinely collected using phased-array (i.e., multi-channel) receivers. For these reasons, the estimation of physiological parameters in model-based MRI is a challenging inverse problem.
In the abstract, the problem of estimating physiological parameters from physics-based signal models in an accelerated MRI framework corresponds to performing a high-dimensional, penalized non-linear least squares (“NLLS”) regression. Although classic “black box” numerical solvers like the Levenberg-Marquardt NLLS iterative routine can be applied for such problems, they are notoriously inefficient and numerically sensitive/unstable. Moreover, since such classic methods are inherently gradient-based (in the sense that they operate by directly marching down the cost functional in the direction of its negative local gradient), they operate poorly for problems where the signal model is not bijective, such as for any phase-based quantitative MRI application that may exhibit “wrapping.”
It would therefore be desirable to provide systems and methods for providing clinicians with quantitative information, despite needing to use imaging modalities that inherently lack or lack complete quantitative information.